Everton will play at home against either Blackpool or Sheffield Wednesday in the fifth round of the FA Cup.
The draw for the last 16 was made on Sunday but the Blues must wait to discover their visitors.
Veteran Kevin Phillips spared Blackpool's blushes with a 93rd-minute penalty on Saturday to earn a 1-1 draw and a replay at Hillsborough.
Everton, meanwhile, secured their safe passage into round five thanks to a 2-1 win over Fulham on Friday.
The Blues have never met Blackpool in the FA Cup, though famously came from two goals down to defeat Wednesday in the final of 1966.
In reaction to the draw, Toffees midfielder Tim Cahill wrote on Twitter: "Love the Fa cup. I'm happy with the draw always a hard draw who ever u face. #timeforanothercuprun."
Youngster Shane Duffy also posted on the social networking site. He said: "Good draw for us in the cup! Hope we can go the full way!!"
Blackpool's last visit to Goodison came in February last year when Louis Saha hit four in a 5-3 home win.
Should Wednesday progress, however, they can look forward to a first trip to the blue half of Merseyside since a 1-1 draw in the 1999/00 season, their last as a Premier League outfit.
Everton and Wednesday have gone toe-to-toe since then, a James McFadden strike and Yakubu brace giving David Moyes' men a 3-0 League Cup third round victory at Hillsborough in September 2007.
The winners of next month's replay will head to Goodison over the weekend of 18/19 February.
The FA Cup fifth round draw in full:
Millwall or Southampton v Bolton
Sunderland or Middlesborough v Arsenal
Norwich v Leicester
Stevenage v Tottenham
Crawley v Stoke
Chelsea v Birmingham
EVERTON v Blackpool or Sheffield Wednesday
Liverpool v Brighton